Constant Temperature Gradient Research Articles

Effect of Solid/Liquid and Eutectic Front Velocities on Microstructure Evolution in Al-20%Cu Alloys

During the solidification process, microstructures are affected by the experimental conditions, the thermophysical characteristics of the alloy, and the type of grain-refining particles. Unidirectional solidification experiments were performed in a vertical Bridgman-type furnace to investigate the effect of the solidification front velocity on the solidified microstructure of a non-refined and refined Al-20%Cu alloy. The samples were solidified by rapidly increasing the sample velocity (v) range from 0.02 mm/s to 0.2 mm/s while maintaining an almost constant temperature gradient (~5 K/mm). As a result, despite changes in the solid/liquid front velocity along the sample, the microstructure of the non-refined alloys remained columnar. In the refined alloy, the columnar structure changed into an equiaxed structure at two different front velocities.

Experimental re-melting of a continental crust: probing the deep storage zone of Campi Flegrei and Vesuvius magmas

Mantle magmas interact with surrounding rocks during their ascent and storage in the continental crust, leading to open system processes as wall rock partial melting. In this study, we have experimentally investigated the reactions between a leucosome depleted migmatite and a primitive K-basaltic of Campi Flegrei (Italy). Experiments were carried out at pressure of 0.8 GPa temperatures from 1250 °C to 1050 °C and constant temperature and thermal gradient conditions. The experimental products consist of biotite-free migmatite, glass and crystals of clinopyroxene, olivine, plagioclase and Cr-spinel with proportions that vary as a function of temperature. Open system isothermal experiments indicate that the chemistry of melts and phase relationships are controlled by the high Al2O3 content of leucosome depleted migmatite with the glass composition shifting from K-trachybasalt towards shoshonite as the temperature decreases from 1200 °C to 1125 °C. At temperatures \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\le$$\\end{document}1150°C, migmatite assimilation is not exclusively due to the assimilation fractional crystallization process because evidence of mingling and mixing is observed. T-gradient experiment shows melt composition ranging from shoshonite to phono-tephrite moving from the slightly crystalline zone (T = 1250 –1210 °C) at the bottom of the capsule towards the highly crystalline zone (T = 1160 –1140 °C). This SiO2-constant trend indicates that at temperature below the basalt solidus, the assimilation of leucosome depleted crust is represented almost exclusively by the biotite breakdown, leading to the increase in Al, Mg, Fe, Ti, and K activities in the system. The shoshonitic composition obtained in our experiments could represent the parental magma for both Campi Flegrei volcanic district and Vesuvius magmatic systems, indicating modification in a deep storage zone through mixing with the partial melts derived from restitic continental crust.

Fluctuation-response relation as a probe of long-range correlations in nonequilibrium quantum and classical fluids.

The absence of a simple fluctuation-dissipation theorem is a major obstacle for studying systems that are not in thermodynamic equilibrium. We show that for a fluid in a nonequilibrium steady state characterized by a constant temperature gradient the commutator correlation functions are still related to response functions; however, the relation is to the bilinear response of products of two observables, rather than to a single linear response function as is the case in equilibrium. This modified fluctuation-response relation holds for both quantum and classical systems. It is both motivated and informed by the long-range correlations that exist in such a steady state and allows for probing them via response experiments. This is of particular interest in quantum fluids, where the direct observation of fluctuations by light scattering would be difficult. In classical fluids it is known that the coupling of the temperature gradient to the diffusive shear velocity leads to correlations of various observables, in particular temperature fluctuations, that do not decay as a function of distance, but rather extend over the entire system. We investigate the nature of these correlations in a fermionic quantum fluid and show that the crucial coupling between the temperature gradient and velocity fluctuations is the same as in the classical case. Accordingly, the nature of the long-ranged correlations in the hydrodynamic regime also is the same. However, as one enters the collisionless regime in the low-temperature limit the nature of the velocity fluctuations changes: they become ballistic rather than diffusive. As a result, correlations of the temperature and other observables are still singular in the long-wavelength limit, but the singularity is weaker than in the hydrodynamic regime.

Ternary eutectic growth and associated tensile properties of directionally solidified Al87Si11Ni2 alloy

The directional growth mechanism and associated tensile properties of ternary Al87Si11Ni2 eutectic alloy were investigated within a wide growth velocity range from 1 to 120 μm s−1 at a constant temperature gradient of 380 K cm−1. If eutectic growth velocity was below 40 μm s−1, this alloy exhibited a ternary lamellar eutectic structure composed of Si plates, Al3Ni chips and αAl matrix. As growth velocity increased to faster regime, the microstructure evolved into a complex structure characterized by primary αAl dendrites plus ternary eutectics. Correspondingly, the preferred crystalline orientation along solidification direction transformed from 101αAl //010Al3Ni // 101Si to 001αAl // 010Al3Ni //113Si. The tensile strength initially increased with the rise of growth velocity until 40 μm s−1, primarily due to the refinement of eutectic structure, and then decreased beyond this threshold, mainly resulting from the coarsening of primary αAl phase.

Effect of Induced Magnetic Field on MHD Flow Between Two Parallel Porous Plates at Constant Temperature Gradient in Presence of Inclined Magnetic Field

Effect of Induced Magnetic Field on MHD Flow Between Two Parallel Porous Plates at Constant Temperature Gradient in Presence of Inclined Magnetic Field

Uticaj temperaturskog gradijenta na savijanje tankih ploča

Within the theory of thermo-elasticity, the temperature field of thin plates is commonly defined via two parameters: temperature in the mid-plane and linear temperature gradient normal to the mid-plane. First, the paper analytically proves the justification of that assumption in machine structures. Then, in an analytical closed form, applying the integral transformation method, the thin plate deflection caused by a constant temperature gradient is defined. It is shown that, in that case, the plate deflection does not depend on its thickness but only on the plate dimensions in the mid-plane. Analytically defined values are compared to corresponding values obtained by applying the thin plate finite element, where the temperature field is described using the two mentioned parameters. This finite element is defined and programmed within the Komips program package. The influence of the temperature gradient on the behavior of constructions mostly depends on the type of material. That is why the behavior of some structural elements made of brass, steel, and concrete is analyzed in this paper.

The influence of thermal dispersion on the initiation of convective instability in Prats flow through a low permeability porous medium

This study investigates the effect of thermal dispersion on the onset of convective thermal instability in a fluid-saturated porous medium. A horizontal throughflow is considered along the layer, which is bounded by two uniformly heated horizontal rigid impermeable walls from above and below. The two walls are maintained at a constant temperature gradient, which is responsible for the buoyancy to occur and thus making the convection happen. Considering thermal dispersion, we have examined how it affects the natural convective instability occurring due to the thermal buoyancy. This paper proposes an entirely new perspective on the accountability of thermal dispersion in the convective instability. The consideration of Prats flow causes the instability in monotonic and oscillatory modes, where in some of the cases, the convection initiates in the oscillatory modes.

Microstructure evolution and mechanical properties of directionally solidified Al0.5CoCr1.3FeNi1.3(Ti, Si, B, C)0.3 multiphase complex concentrated alloy

Microstructure evolution and mechanical properties of Al0.5CoCr1.3FeNi1.3(Ti, Si, B, C)0.3 multiphase complex concentrated alloy (CCA) prepared by directional solidification combined with quenching during solidification (QDS) technique were studied. The directionally solidified (DS) samples were prepared at constant growth rates V ranging from 2.78 × 10−6 to 5.56 × 10−5 m/s, the constant temperature gradient in liquid at the solid-liquid interface of GL = 16.5 × 103 °C/m and then quenched at a cooling rate of about 50 °C/s. The solidification of the studied CCA begins with the growth of columnar FCC(A1) dendrites and is finalised by the formation of a multiphase microstructure in the interdendritic region. The DS samples subjected to isothermal annealing at 900 °C for 25 h show a strong brittle-ductile transition (BDT) behaviour characterised by brittle-ductile transition temperature (BDTT) between 650 and 700 °C at a strain rate of 1 × 10−4 s−1. The tensile deformation curves show only a strain hardening stage at test temperatures up to 650 °C. At temperatures ranging from 750 to 900 °C, the alloy shows anomalous strain hardening behaviour characterised by one strain hardening stage and three well-distinguished strain softening stages.

Simulation of dendritic grain structures with Cellular Automaton–Parabolic Thick Needle model

This article presents advances and computing optimizations on the CAPTN model which couples the Cellular Automaton (CA) and the Parabolic Thick Needle (PTN) methods. This optimized CAPTN model, which is developed in 2D for now, is evaluated on its ability to reproduce two physical quantities developed during directional growth in a constant temperature gradient G with isotherm velocity vL: the interdendritic primary spacing and the grain boundary orientation angle between two grains of different orientations. It is shown that the CAPTN model can reproduce selection between primary branches and creation of new branches from tertiary branches as long as cell size is sufficiently small to model solute interactions between branches. In these conditions, simulations converge toward a distribution of primary branches which depends on the history of the branching events, as has been observed in experimental studies. Average primary spacing obtained tends to decrease with G and vL, in agreement with the theoretical G−bvL−c power law. Contrary to the classical CA model, the grain boundary orientation angle obtained in CAPTN simulations is stable with cell size and in good agreement with previous phase field studies for various gradients. Moreover, the grain boundary orientation angle is found to follow an exponential law with the ratio G/vL.

Study on Solidification and Phase Transformation Behaviors in Ni-based Superalloy IN625

The solidification and phase transformation behaviors of IN625 with low C and Fe were investigated through directional solidification and quenching experiments. The primary and secondary dendrite arm spacing decreased exponentially as the solidification rate increased, demonstrating good agreement with theoretical equations. The MC carbide formed at a constant temperature gradient regardless of the solidification rate. It is reasonable to assume that the Laves phase solidified in the final stage of solidification, as it was found at the bottom of the mushy zone. The morphologies and sizes of the MC carbide and the Laves phase were closely related to the solidification rate. Increasing the solidification rate at a constant thermal gradient resulted in the development of the MC carbide from blocky to Chinese script, and eventually spotty shapes, along with decreasing size. As a result of this research, it is believed that the weldability of the alloy could be improved at the expense of mechanical properties, especially with low C and Fe contents and a relatively high solidification rate, which are able to generate the finely distributed MC and Laves phase.

Directional lateral crystallization of vacuum-deposited C8-BTBT thin films via liquid crystal phase by a seeded horizontal temperature gradient cooling technique

C8-BTBT thin films with large domain sizes were grown by vacuum deposition and subsequent post-annealing and cooling crystallization via liquid crystal phase with a constant horizontal temperature gradient.

Quantitativeness of phase-field simulations for directional solidification of faceted silicon monograins in thin samples.

We report the results of a two-dimensional reference model for the formation of facets on the left and right side of a silicon monograin that is solidified by pulling a thin sample in a constant temperature gradient. Anisotropy functions of both the surface energy and the kinetic attachment coefficient are adapted from a recent model for free growth of silicon micrometer-sized grains [Boukellal et al., J. Cryst. Growth 522, 37 (2019)0022-024810.1016/j.jcrysgro.2019.06.005.]. More precise estimates of the physical parameters entering these functions are obtained by reanalyzing available experimental results. We show that the reference model leads to a differential equationfor the shape of the solid-liquid interface. The numerical solutions of this equationgive a reference law Λ(V_{f}) relating the facet length Λ to the facet normal velocity V_{f}. In parallel, phase-field simulations of the reference model are performed for two growth orientations, [001] and [011]. Facet lengths Λ obtained from simulations at different facet velocities are first extrapolated to the limit of vanishing interface width. This extrapolation is made possible by constructing a master curve common to the whole range of V_{f} values considered. The extrapolated Λ values are then compared with the ones predicted by the Λ(V_{f}) reference law. Both sets give comparable values, with an accuracy of a few percent, which confirms that the phase-field model can give quantitative results for faceted solidification of silicon.

Rayleigh-Bénard-Marangoni Instability in a Self-rewetting Fluid Layer Overlying a Porous Medium

Rayleigh-Bénard-Marangoni instability in a bilayer system of self-rewetting fluid overlying a porous medium is investigated. The upper surface of the fluid layer is assumed non-deformable and a constant temperature gradient is imposed. Unlike in previous works, self-rewetting fluid is considered in this paper, whose surface tension is a quadratic function of temperature. As a result, it would reinforce or suppress the instability caused by buoyancy in different scenarios. Thorough study is carried out and the influence of depth ratio h, Rayleigh number Ra and Biot number Bi on instability of the system is discussed. It was found that the marginal curve is bimodal in certain combination of parameters and mode transition of convection is also found.

Effect of Temperature Gradient on Chloride Ion Diffusion in Nuclear Reactor Containment Building Concrete

Chloride diffusion through concrete is influenced by harsh environmental conditions such as high ambient temperature and relative humidity. This paper examined the influence of temperature gradient on chloride diffusion in concrete under high ambient temperature conditions. Chloride diffusion tests using cylindrical concrete samples were performed in constant temperature and temperature gradient conditions. In a temperature gradient condition, a much higher chloride concentration was measured than at constant temperatures, which could not be explained only by the mass diffusion driven by the concentration gradient. A new analytical model of chloride diffusion with the mass diffusion term including the temperature effect and the thermo-diffusion term including the temperature gradient effect was applied to the results, which showed that the thermo-diffusion contribution was significant. Using the analytical model with the mass diffusion (DCl) and thermo-diffusion (DT) coefficients, the service life of reactor containment buildings (RCBs) in nuclear power plants (NPPs) in the Middle Eastern and North African (MENA) region was estimated. The results showed that the service life of the RCBs could be reduced by the temperature gradient, indicating the possible application of the proposed analytical model.

Frost heave in coarse-grained soils: experimental evidence and numerical modelling

Frost heave in coarse-grained soils caused by vapour transfer has attracted much attention, but little experimental or numerical evidence has been reported thus far. A series of laboratory experiments is carried out by a frost heave apparatus and an X-ray micro-computed tomography instrument. The only water supply mechanism to the tested specimen is vapour transfer. The results indicate that considerable frost heave occurs in coarse-grained soil specimens with a zero fines content. The ratio of frost heave to the initial height can reach 13·8% and 25·1% at 14 days and 18 days, respectively. Ice crystals first grow in pores causing the soil particle to rotate and move, and the soil porosity to increase. With continued ice crystal growth, they eventually become connected and form an ice lens. If a constant temperature gradient is applied, only one horizontal ice lens is formed, which differs from the layered ice lenses observed in fine-graded soils. A new numerical model is developed to simulate ice formation and frost heave in coarse-grained soils, which considers the process of vapour transfer and desublimation. The predicted frost heave results agree well with the measured results. This study provides a novel explanation for the frost heave mechanism in coarse-grained soils.

THERMAL EFFECT ON BUBBLE RISE – AN EXPERIMENTAL STUDY

This paper presents the findings of an experimental study on the effect of temperature gradient on bubble rise velocity in water. At the bottom of the chamber holding water, a bubble (equivalent diameter, req 1 mm) is created and rises through it. At a height of 60 cm from the chamber’s bottom, a high-speed camera (1000 fps, Kodak, Model 1000 HRC) is mounted with a 90 mm Macro lens. It is connected to a computer. For image capture and processing, the commercial tools Sigma Scan Pro 5.0 and Adobe Photoshop are used. The chamber can be heated with infrared light, resulting in a constant temperature gradient of 1.10C/cm between 30 and 40 cm above the needle in the water. Bubble rise characteristics, such as bubble size and rise velocity, are determined both in the presence and absence of a temperature gradient. The current study clearly demonstrates that this gradient causes an additional increase in terminal rise velocity.

Dependence of Microstructures and Mechanical Properties on the Growth Rate and Composition in Directionally Solidified Mg-Gd Alloys

Microstructures and mechanical properties of directionally solidified Mg-xGd (5.21, 7.96 and 9.58 wt.%) alloys were investigated at a wide range of growth rates (V = 10-200 μm/s) under the constant temperature gradient (G = 30 K/mm). The results showed that when the growth rate was 10 μm/s, different interface morphologies were observed in three tested alloys: cellular morphology for Mg-5.21Gd alloy, a mixed morphology of cellular structure and dendritic structure for Mg-7.96Gd alloy and dendrite morphology for Mg-9.58Gd alloy, respectively. Upon further increasing the growth rate, only dendrite morphology was exhibited in all experimental alloys. The microstructural parameters (λ1, λ2) decreased with increasing the growth rate for all the experimental alloy, and the measured λ1 and λ2 values were in good agreement with Trivedi model and Kattamis-Flemings model, respectively. Vickers hardness and the ultimate tensile strength increased with the increase of the growth rate and Gd content, while the elongation decreased gradually. Furthermore, the relationships between the hardness, ultimate tensile strength, the growth rate and the microstructural parameters were discussed and compared with the previous experimental results.

Insight into the relationship between unsteady Cattaneo-Christov double diffusion, random motion and thermo-migration of tiny particles

• Unsteady bidirectional flow of Newtonian nanofluid is investigated with the expressions of Cattaneo-Christov double diffusion. • Thermal convective and Nield’s conditions are in action. • Random movement and thermo-migration of tiny-particles have been used for the inspection of heat/mass transferences activities. • Keller-Box approach was adopted to solve the modeled equations. Significant impact of unsteady Cattaneo-Christov double diffusion, random motion and thermo-migration of tiny particles on thermal storage and in heat exchangers devices has attracted us to investigate the role of these thermal engineering terms in the existence of convectively heating and zero-mass flux at the bidirectionally stretchable wall. Combination of similarity expressions is adopted to transform the prevailing partial differential equations into ordinary differential equations and then solved, numerically, by using Keller-Box simulation technique. Temperature and concentration phases are discussed under the influences of involved parameters, graphically. It is detected that thermal relaxation dependent on heat flux maximizes the temperature gradient, whereas thermal relaxation dependent on mass flux minimizes the concentration gradient. It is also scrutinized that escalating choice of random motion of tiny particles provides constant temperature gradient because of Nield’s expression. Moreover, augmenting choice of thermo-migration of tiny particles enhances the concentration gradient. Furthermore, intensifying choice of unsteady factor abridges the temperature plus concentration distributions and also it condenses all the three boundary layer thicknesses.

On a Spectral Problem for Convection Equations

Spectral problems for stationary unidirectional convective flows in vertical heat exchangers at various boundary temperature conditions are considered. The constant temperature gradient on the vertical walls is used as a spectral parameter. The heat exchanger cross-section can be of an arbitrary shape. The general properties of the spectral problem solutions are established. Solutions are obtained in an analytical form for rectangular and a circular cross sections. The critical values of temperature gradient at which convective flow arises are found. The corresponding vertical velocity profiles are constructed. The properties of solutions of a new transcendental equation for the spectral values are studied

Metamaterials simulation for thermal diffusers

The heat extraction efficiency of a cylindrical diffuser can be optimized by applying differential geometry [J.-P. Huang, Theoretical Thermotics: Transformation Thermotics and Extended Theories for Thermal Metamaterials (Springer, 2020)], in order to find a metamaterial design. That can be done by coupling a thermally insulating material (polytetrafluoroethylene) with a high thermal conductivity material (copper) where the heat flow is directed. By controlling the distance between the isothermal contours, to extract the heat while maintaining a constant temperature gradient along the diffuser avoiding heat accumulation.